Burnap started his career in productions from the
Public Theatre. In 2014, he was part of the ensemble in the revival of
King Lear starring
John Lithgow,
Annette Bening and
Yahya Abdul-Mateen II. In 2016, he starred as
Troilus in
Troilus and Cressida. He gained prominence for his role as Toby Darling in the
Matthew Lopez play
The Inheritance, which premiered in the
West End and transferred to
Broadway, for which he won the
Tony Award for Best Actor in a Play. In 2022, Burnap starred as Phil in the
Apple TV+ series
WeCrashed opposite
Anne Hathaway and
Jared Leto, and as
Joseph Smith in the
FX on Hulu limited series
Under the Banner of Heaven with
Andrew Garfield and
Daisy Edgar-Jones. In 2023, he portrayed
King Arthur in the Broadway revival of the
Lerner and Loewe musical
Camelot. Burnap starred opposite
Phillipa Soo as
Guinevere in the revival with a new book by
Aaron Sorkin. For his performance, he was nominated for the
Drama Desk Award for Outstanding Lead Performance in a Musical. Later that year, he portrayed Joris Ivens in the off-Broadway play
Spain written by
Jen Silverman, where he acted opposite
Marin Ireland. The play revolves around the complications of filming a movie financed by the Russian government during the
Spanish Civil War. In 2025, he played Jonathan, a character based on
Prince Charming, in the live-action
Disney remake
Snow White, where he starred opposite
Rachel Zegler and
Gal Gadot. ==Acting credits==